Stochastic quantization and large N

In quantum field theory, large N problem refers to a class of important questions regarding the asymptotic behavior of a model with N field components when N goes to infinity. Through stochastic quantization, one relates the large N problem with singular stochastic PDE and mean field limit theory. By combining ideas from these fields one can prove interesting results regarding the dynamic, the quantum fields, the observables, and so on. In this talk we will focus on the linear sigma model, which is an N-vector Phi4 type quantum field theory. In particular we prove some predictions by physicists such as Wilson, and we discover some new probabilistic descriptions in the large N limit. Based on joint works with Scott Smith, Rongchan Zhu and Xiangchan Zhu.